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Question

In the fig. the potentiometer wire AB of length L & resistance 9 r is joined to the cell D of e.m.f. ε and internal resistance r. The cell Cs e.m.f. is ε/2 and its internal resistance is 2 r. The galvanometer G will show no deflection then find length AJ:
1021093_ef41eb13140a4980a477c16f25f04a7e.png

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Solution

Let at x distance it will show no deflection-
then current on AB=ε10r
In case of no deflection-
9rLX×ε10r=ε10r
So,x=5L9

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